Practice Test 3 - AP Statistics

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A company wants to test whether a new training program improves employee typing speed compared with the current program. Employees work in two departments (Sales and Support), and the company suspects departments differ in baseline typing speed due to job tasks. The company can train each employee using only one program, and wants to compare programs fairly while reducing variability. Which experimental design is most appropriate?
2. A sleep researcher tests whether the mean number of hours of sleep per night for students at a certain college is less than 7 hours. A random sample of 25 students is selected, and conditions for a one-sample $t$ test are met. The hypotheses are $H_0: \mu=7$ and $H_a: \mu<7$ with $\alpha=0.01$. The test is completed and the p-value is 0.084. What conclusion is appropriate?
3. A city planner collected data from $n=32$ intersections on average daily traffic volume (in thousands of cars, $x$) and average wait time at the light (in seconds, $y$). A least-squares regression of wait time on traffic volume produced slope $b_1=2.4$ seconds per 1,000 cars. To test whether there is a linear relationship, the planner performed a slope test with hypotheses $H_0: \beta_1=0$ versus $H_a: \beta_1\ne 0$ at $\alpha=0.05$ and obtained a p-value of $0.018$. Based on this completed test, what conclusion is appropriate?
4. A company has 600 employees, and 40% work remotely at least one day per week. Many SRSs of $n=75$ employees are taken without replacement and $\hat p$ is recorded. Which statement about the sampling distribution is correct?
5. A city wants to estimate the mean number of minutes commuters spend on public transit each weekday for all city residents who commute. Surveyors stand at one downtown subway station from 7:00–8:00 a.m. on a Tuesday and ask every 5th rider entering the station how long their commute is. The city reports the result as representing all commuters in the city. Which issue most threatens the validity of this sampling method?
6. A researcher is studying whether background music affects reading comprehension. She recruits 90 students from an introductory psychology class. Students are randomly assigned to one of three treatments while reading the same passage: no music, instrumental music, or music with lyrics. After reading, students take the same comprehension quiz; the response variable is quiz score. Which improvement would best reduce the impact of confounding due to students' prior reading ability?
7. A student randomly chooses one course from a list. Let Event $A$ be "the course is an AP course," and Event $B$ be "the course meets in the morning." The school counselor states: "$P(A\cup B)$ can be found by adding $P(A)$ and $P(B)$." Which statement about Events $A$ and $B$ is correct?
8. A doctor gives a new treatment to 12 patients and records whether each patient's symptoms improve. A success is "improves," and exactly 12 patients are treated, but patients have very different conditions and severity levels, leading to different probabilities of improvement. Does this meet binomial conditions?
9. In a factory, a randomly selected item is inspected. Let event $A$ be "the item is defective," and event $B$ be "the item came from Machine 2." Machine 2 is known to produce a higher defect rate than the overall factory average. How does knowing that $B$ occurred affect the likelihood of $A$?
10. A school principal claims that at least 80% of students eat breakfast on school days. In a random sample of 250 students, a 90% confidence interval for the true proportion of all students who eat breakfast is $(0.77, 0.83)$. Is the claim supported by the confidence interval?
11. A website runs an email campaign to exactly 500 subscribers. A success is a subscriber clicking the link in the email; a failure is not clicking. The subscribers are all in the same small office, and coworkers often talk, so one person clicking may influence others to click. Does this meet binomial conditions for modeling the number of clicks?
12. A city health department tests whether the proportion of local restaurant inspections that result in a "critical violation" citation has dropped after a new training program. Based on a random sample of recent inspections, the department plans to decide whether to expand the program citywide or cancel it. If the inference is wrong, the city could either waste a large budget on an ineffective program or fail to reduce foodborne illness risk. Why is it important to consider potential error when making this decision from sample data?
13. A biology teacher recorded the number of seeds germinated (out of 50) for each of 32 trays under the same conditions. The dotplot below shows the distribution of germinated-seed counts. Which statement best describes the distribution?
14. A manager regresses weekly sales ($y$, dollars) on number of employees scheduled ($x$). The manager claims, "Scheduling more employees increases mean weekly sales." A 98% confidence interval for the slope is $( -55,\ -10)$ dollars per employee. Is the claim supported by the confidence interval?
15. A coffee shop gives a scratch-off card with each purchase. Each card has exactly one outcome printed on it: "Free drink," "$1 off," or "No prize." The manager says that for a randomly selected card, the probability of "Free drink" is $0.08$. Let the sample space be {Free drink, $1 off, No prize} and consider the event F = {Free drink}. Which statement correctly describes the probability $P(F)=0.08$?
16. A gym wants to estimate the mean number of days per week that all members exercise. The gym prints a list of all members and selects every 25th name, starting with a randomly chosen starting point, and surveys those selected members. Which statement best describes the sample representativeness?
17. A voter advocacy group suspects that fewer than 65% of eligible voters in a state are registered to vote. In a random sample of 400 eligible voters, 248 were registered. A one-proportion $z$ test was conducted for $H_0: p=0.65$ versus $H_a: p<0.65$ at $\alpha=0.05$. The test gave a $p$-value of 0.021, so the group rejected $H_0$. Which conclusion is appropriate?
18. A university states that the mean time to graduate for its students is 4.0 years. A student group believes the mean time to graduate is more than 4.0 years. A random sample of $n=60$ recent graduates is selected, and the sample mean time to graduate is $\bar{x}=4.3$ years. Which hypotheses are appropriate for a test of the population mean time to graduate, $\mu$?
19. For the population of all bottles filled by a machine, the amount of liquid (in ounces) is approximately Normal with mean $\mu=20.0$ oz and standard deviation $\sigma=0.4$ oz. The interval from 19.6 oz to 20.4 oz is marked on the normal curve. Which statement about the marked interval is correct?
20. A fitness app company analyzes the resting heart rates (beats per minute) from a random sample of 55 adult users who recorded measurements under similar conditions. The distribution is roughly symmetric with a single peak. Why is a normal model reasonable for these resting heart rates?

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